{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# -*- coding: utf-8 -*-\n",
    "# @author: tongzi\n",
    "# @created date: 2019/10/15\n",
    "# @description: Gaussian mixture model\n",
    "# @last modification: 2019/10/15"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import Libraries\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "from scipy import stats\n",
    "%matplotlib inline\n",
    "sns.set()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5.12.1 k-means算法的缺陷  \n",
    "下面来介绍一些 k-means 算法的不足之处，并思考如何改进我们的聚类模型。就像前一节所看到的，只要给定简单且分离性非常好的数据，k-means 就可以找到合适的聚类结果。  \n",
    "  \n",
    "例如，只要有简单的数据簇，k-means 算法就可以快速给这些簇作标记，标记结果和通过肉眼观察到的簇的结果十分接近："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.datasets.samples_generator import make_blobs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "X, y_true = make_blobs(n_samples=400, centers=4, \n",
    "                       cluster_std=0.60, random_state=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.cluster import KMeans"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "kmeans = KMeans(n_clusters=4, random_state=0)\n",
    "labels = kmeans.fit_predict(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x216a580ceb8>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X[:, 0], X[:, 1], c=labels, s=40, cmap='viridis')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "通过直接观察可以发现，某些点的归属簇比其他点的归属簇更加明确。例如，中间的两个簇似乎有一小块区域重合，因此我们对重合部分的点将被分配到哪个簇不是很有信心。不幸的是，k-means 模型本身也没有度量簇的分配概率或不确定性的方法（虽然可以用数据重抽样方法 bootstrap 来估计不确定性）。因此，我们必须找到一个更通用的模型。  \n",
    "  \n",
    "理解 k-means 模型的一种方法是，它在每个簇的中心放置了一个圆圈（在更高维空间中是一个超空间），圆圈半径根据最远的点与簇中心点的距离算出。这个半径作为训练集分配簇的硬切断（hard cutoff），即在这个圆圈之外的任何点都不是该簇的成员。可以用以下函数将这个聚类模型可视化:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.cluster import KMeans\n",
    "from scipy.spatial.distance import cdist\n",
    "def plot_kmeans(kmeans, X, n_clusters=4, rseed=0, ax=None):\n",
    "    labels = kmeans.fit_predict(X)\n",
    "    \n",
    "    ax = ax or plt.gca()\n",
    "    # plot the original data\n",
    "    ax.scatter(X[:, 0], X[:, 1], c=labels, s=40, cmap='viridis',\n",
    "               zorder=2)\n",
    "    ax.axis('equal')\n",
    "    \n",
    "    # plot the model of kmeans\n",
    "    centers = kmeans.cluster_centers_\n",
    "    radius = [cdist(X[labels==i], [center]).max()\n",
    "             for i, center in enumerate(centers)]\n",
    "    \n",
    "    for center, r in zip(centers, radius):\n",
    "        ax.add_patch(plt.Circle(center, r, fc='#CCCCCC',\n",
    "                               lw=3, alpha=0.6, zorder=1))\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "kmeans = KMeans(n_clusters=4, random_state=0)\n",
    "plot_kmeans(kmeans, X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "k-means 有一个重要特征，它要求这些簇的模型必须是圆形：k-means 算法没有内置的方法来实现椭圆形的簇。因此，如果对同样的数据进行一些转换，簇的分配就会变得混乱:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "rng = np.random.RandomState(13)\n",
    "X_stretched = X @ rng.rand(2, 2)\n",
    "\n",
    "kmeans = KMeans(n_clusters=4, random_state=0)\n",
    "plot_kmeans(kmeans, X_stretched)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "通过肉眼观察，可以发现这些变形的簇并不是圆形的，因此圆形的簇拟合效果非常糟糕。总之，k-means 对这个问题有点无能为力，只能强行将数据拟合至 4 个圆形的簇，但却导致多个圆形的簇混在一起、相互重叠，左下部分尤其明显。有人可能会想用 PCA（详情请参见 5.9 节）先预处理数据，从而解决这个特殊的问题。但实际上，PCA 也不能保证这样的全局操作不会导致单个数据被圆形化。  \n",
    "  \n",
    "k-means 的这两个缺点——类的形状缺少灵活性、缺少簇分配的概率——使得它对许多数据集（特别是低维数据集）的拟合效果不尽如人意。  \n",
    "  \n",
    "你可能想通过对 k-means 模型进行一般化处理来弥补这些不足，例如可以通过比较每个点与所有簇中心点的距离来度量簇分配的不确定性，而不仅仅是关注最近的簇。你也可能想通过将簇的边界由圆形放宽至椭圆形，从而得到非圆形的簇。实际上，这正是另一种的聚类模型——高斯混合模型——的两个基本组成部分。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5.12.2一般化EM算法：高斯混合模型  \n",
    "一个高斯混合模型（Gaussian mixture model，GMM）试图找到多维高斯概率分布的混合体，从而获得任意数据集最好的模型。在最简单的场景中，GMM 可以用与 k-means 相同的方式寻找类："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.mixture import GaussianMixture"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x216a6aaf588>"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "gmm = GaussianMixture(n_components=4).fit(X)\n",
    "labels = gmm.predict(X)\n",
    "plt.scatter(X[:, 0], X[:, 1], c=labels, s=50, cmap='viridis')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "但由于 GMM 有一个隐含的概率模型，因此它也可能找到簇分配的概率结果——在 Scikit-Learn 中用 predict_proba 方法实现。这个方法返回一个大小为 [n_samples, n_clusters]的矩阵，矩阵会给出任意点属于某个簇的概率："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(400, 4)\n",
      "[[0.    0.    0.463 0.537]\n",
      " [1.    0.    0.    0.   ]\n",
      " [1.    0.    0.    0.   ]\n",
      " [0.    0.    0.    1.   ]\n",
      " [1.    0.    0.    0.   ]]\n"
     ]
    }
   ],
   "source": [
    "proba = gmm.predict_proba(X)\n",
    "print(proba.shape)\n",
    "print(proba[:5].round(3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "我们可以将这个不确定性可视化，用每个点的大小体现预测的不确定性，使其成正比。由下图可知，在簇边界上的点反映了簇分配的不确定性："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "size = 50 * proba.max(1) ** 3 # 取立方强调差异"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x216a76ddda0>"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X[:, 0], X[:, 1], c=labels, s=size, cmap='viridis')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "高斯混合模型本质上和 k-means 模型非常类似，它们都使用了期望最大化方法，具体实现如下。\n",
    "(1) 选择初始簇的中心位置和形状。  \n",
    "(2) 重复直至收敛。  \n",
    "&emsp;&emsp;a. 期望步骤（E-step）：为每个点找到对应每个簇的概率作为权重。  \n",
    "&emsp;&emsp;b. 最大化步骤（M-step）：更新每个簇的位置，将其标准化，并且基于所有数据点的权重来确定形状。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "最终结果表明，每个簇的结果并不与硬边缘的空间（hard-edged sphere）有关，而是通过高斯平滑模型实现。正如在 k-means 中的期望最大化方法，这个算法有时并不是全局最优解，因此在实际应用需要使用多个随机初始解。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "from matplotlib.patches import Ellipse\n",
    "def plot_ellipse(position, covariance, ax=None, **kwargs):\n",
    "    ax = ax or plt.gca()\n",
    "    \n",
    "    # convert covraiance to the main axis\n",
    "    # 将协方差转换成主轴\n",
    "    if covariance.shape == (2, 2):\n",
    "        U, s, Vt = np.linalg.svd(covariance)\n",
    "        angle = np.degrees(np.arctan2(U[1, 0], U[0, 0]))\n",
    "        width, height = 2 * np.sqrt(s)\n",
    "    else:\n",
    "        angle = 0\n",
    "        width, height = 2 * np.sqrt(covariance)\n",
    "        \n",
    "    # draw ellipse\n",
    "    for nsig in range(1, 4):\n",
    "        ax.add_patch(Ellipse(position, nsig * width, \n",
    "                             nsig * height, angle, **kwargs))\n",
    "\n",
    "def plot_gmm(gmm, X, label=True, ax=None):\n",
    "    ax = ax or plt.gca()\n",
    "    labels = gmm.fit_predict(X)\n",
    "    if label:\n",
    "        ax.scatter(X[:, 0], X[:, 1], c=labels, s=50, \n",
    "                   cmap='viridis', zorder=2)\n",
    "    else:\n",
    "        ax.scatter(X[:, 0], X[:, 1], s=50, zorder=2)\n",
    "    ax.axis('equal')\n",
    "    w_factor = 0.2 / gmm.weights_.max()\n",
    "    for pos, covar, w in zip(gmm.means_, gmm.covariances_, gmm.weights_):\n",
    "        plot_ellipse(pos, covar, alpha=w * w_factor)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "gmm = GaussianMixture(n_components=4, random_state=42)\n",
    "plot_gmm(gmm, X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "同理，也可以用 GMM 方法来拟合扩展过的数据集。高斯模型允许使用全协方差（full\n",
    "covariance），即使是于非常扁平的椭圆形的簇，该模型也可以处理:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "gmm = GaussianMixture(n_components=4, covariance_type='full', \n",
    "                      random_state=42)\n",
    "plot_gmm(gmm, X_stretched)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 选择方差的类型  \n",
    "如果仔细观察前面的拟合结果，你会发现每个拟合的 covariance_type 选项的设置是不同的。这个超参数控制了每个簇的形状自由度，其设置对任何问题都非常重要。它的默认设置是 covariance_type=\"diag\" ，意思是簇在每个维度的尺寸都可以单独设置，椭圆边界的主轴与坐标轴平行。另一个更简单、更快的模型是 covariance_type=\"spherical\" ，该模型通过约束簇的形状，让所有维度相等。这样得到的聚类结果和 k-means 聚类的特征是相似的，虽然两者并不完全相同。还有一个更复杂、计算复杂度也更高的模型（特别适应于高维度数据）是 covariance_type=\"full\" ，该模型允许每个簇在任意方向上用椭圆建模。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5.12.3将GMM用于密度估计  \n",
    "虽然 GMM 通常被归类为聚类算法，但它本质上是一个密度估计算法；也就是说，从技\n",
    "术的角度考虑，一个 GMM 拟合的结果并不是一个聚类模型，而是描述数据分布的生成\n",
    "概率模型。  \n",
    "例如从 Scikit-Learn 的 make_moons 函数生成的一些数据："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x216ad61dcf8>"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.datasets import make_moons\n",
    "Xmoon, ymoon = make_moons(200, noise=0.05, random_state=0)\n",
    "plt.scatter(Xmoon[:, 0], Xmoon[:, 1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "如果用 GMM 对数据拟合出两个成分，那么作为一个聚类模型的结果，其实没什么用:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "gmm2 = GaussianMixture(n_components=2, covariance_type='full', \n",
    "                       random_state=0)\n",
    "plot_gmm(gmm2, Xmoon)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "但如果选用更多的成分而忽视簇标签，就可以找到一个更接近输入数据的拟合结果:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "gmm16 = GaussianMixture(n_components=16, covariance_type='full', \n",
    "                       random_state=0)\n",
    "plot_gmm(gmm16, Xmoon)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "这里采用 16 个高斯曲线的混合形式不是为了找到数据的分隔的簇，而是为了对输入数据\n",
    "的总体分布建模。这就是分布函数的生成模型——GMM 可以为我们生成新的、与输入数\n",
    "据类似的随机分布函数。例如，下面是用 GMM 拟合原始数据获得的 16 个成分生成的 400个新数据点:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x216ad7ef518>"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Xnew, ynew = gmm16.sample(n_samples=400)\n",
    "plt.scatter(Xnew[:, 0], Xnew[:, 1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "GMM 是一种非常方便的建模方法，可以为数据估计出任意维度的随机分布。\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 需要多少成分？  \n",
    "作为一种生成模型，GMM 提供了一种确定数据集最优成分数量的方法。由于生成模\n",
    "型本身就是数据集的概率分布，因此可以利用该模型来评估数据的似然估计，并利用\n",
    "交叉检验防止过拟合。还有一些纠正过拟合的标准分析方法，例如用赤池信息量准则\n",
    "（Akaike information criterion，AIC，https://en.wikipedia.org/wiki/Akaike_information_\n",
    "criterion）、贝叶斯信息准则（Bayesian information criterion，BIC，https://en.wikipedia.org/wiki/Bayesian_information_criterion）调整模型的似然估计。Scikit-Learn 的 GMM 评估器已经内置了以上两种度量准则的计算方法，在 GMM 方法中使用它们很方便。下面用 AIC 和 BIC 分别作为月球数据集的 GMM 成分数量的函数："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x216ad8df5c0>"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_components = np.arange(1, 21)\n",
    "models = [GaussianMixture(n ,covariance_type='full', random_state=0).fit(Xmoon) \n",
    "          for n in n_components]\n",
    "plt.plot(n_components, [m.bic(Xmoon) for m in models], label='BIC')\n",
    "plt.plot(n_components, [m.aic(Xmoon) for m in models], label='AIC')\n",
    "plt.xlabel('n_components')\n",
    "plt.legend(loc='best')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "类的最优数量出现在 AIC 或 BIC 曲线最小值的位置，最终结果取决于我们更希望使用哪一种近似。AIC 告诉我们，选择 16 个成分可能太多，8 个 ~12 个成分可能是更好的选择。由于这类经典问题的存在，BIC 推荐了一个更简单的模型。  \n",
    "  \n",
    "这里需要注意的是：成分数量的选择度量的是 GMM 作为一个密度评估器的性能，而不是\n",
    "作为一个聚类算法的性能。建议你还是把 GMM 当成一个密度评估器，仅在简单数据集中\n",
    "才将它作为聚类算法使用."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5.12.4例子：用GMM生成新的数据  \n",
    "前面介绍了一个将 GMM 作为数据生成模型的示例，目的是根据输入数据的分布创建一个\n",
    "新的样本集。这次还利用这个思路，为前面使用过的标准手写数字库生成新的手写数字。首先，用 Scikit-Learn 的数据工具导入手写数字数据："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.datasets import load_digits"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1797, 64)"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "digits = load_digits()\n",
    "digits.data.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 画出前100个数据\n",
    "def plot_digits(data):\n",
    "    fig, ax = plt.subplots(10, 10, figsize=(8, 8), \n",
    "                           subplot_kw=dict(xticks=[], yticks=[]))\n",
    "    fig.subplots_adjust(hspace=0.05, wspace=0.05)\n",
    "    for i, ax in enumerate(ax.flat):\n",
    "        im = ax.imshow(data[i].reshape(8, 8), cmap='binary')\n",
    "        im.set_clim(0, 16)\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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xMRHE1PqFuo7R0VF5zJGRkW3//+9+97ut/9PVvGdPWE6Tk5PexwP27dsXxNS1ZbK7429rVD1PT08Hsc7ctcDVqo6tNJiZra6uBjF1jwpR5PlT9aiuT11bi1opolmdd3x8vMShFVmavZwo/8HevXvbKYqTpdkbk9TWdwo1znl5+O2YPTQ0tPV/Sr1N+1meMLOfktTtDE5+/Yvmugya5pNm9sQGq54HLcdmaO4VaK7P1pixjab/zFw0s+/N7Gcz+6WSqBJ8Y2bf2q96zdBci0HT3Kl3EOp50HJshuZegeb6dOrdBm+W/QXN9eHNsjeguTeguT7Zb5avU4/8/PlzGb9y5UoQU/9WPjMzE8QuXryYevotkvU2sby8HMROnDiR9N0nT4L8mpm+5q9kaVa7cnjxhYWFIHbmzJmc03m4mtU60u3bt+Vnnz59GsRUHan1i5s3b8pjqjqy/9NbpD46OXfuXBBT+mK/Ue0gS6vSYObmI0DluPbzp2rFTF+L+qyq76NHj+ZIMCtUE+r5u3//ftJ37927J+Olxgw1BpvpnKp7nlpDEbI037hxQ8bVmDE7OxvEWtRuJ1Jv02T5JfXInz59kvFXr14FMWVS8R6cTJL1NvH58+cg9vLly9bfjZCl2fuBsdK3traWqyUVV/PGxkYQ8zS/efMmiC0tLQUxZVRaX19vFNjBl46/RVHX0aIOOsnSqjSY+bmvRJZmVStmesxQ1+GNOZkUqQmlT/1Ht6L2mPHu3TsZV5ozn6scsjSvrKzIuKqNQnNHJ1IvPx0BAACIwGQJAAAQociPrrwdwFX/VBVTu1h7O6bX7vO4k3cL9/p6qr6HKn8NZq4iqNx5u5ur3pQq9uOPPwYxr97UZ0uielaqay7VC1ih8vn48WP5WRVXtdKPPqbe+rsaH1Svz5o5zkWNSSqn6vlVvXC9z5ZEPSupY5/3nJW6J96YoWpD9YtVY1+JeYM3SwAAgAhMlgAAABGYLAEAACIwWQIAAETINvioxV1l0DEzm5ubC2LKnOFtBFsKZZbxFpE980gnp06dCmIlzUdqsdzLkzKeqM+qay6Z+9QNpz3U70XV92tv/uwZGC5cuBDE1ObWyrySWlcxVF14DabV/e6HMUYZR65fv578fVXftY1+Oah6VDGlufb98PKUakBS388x7ZVEGb2U6Uc9vyXGDN4sAQAAIjBZAgAARGCyBAAAiMBkCQAAEIHJEgAAIEKRdnceXkurTlJ39WiLctOpNkk7Ha81lnL7KpfYTnIQqnuu3G7KYVvbDevlWbm71WeHhoaCmJf73GtR99Ujtd1dbXJ2P6ntMk9FOXjVOGKm3aHqmlXN1742z4WtnivlzE1t5VcS75lQbnSFumbcsAAAAD2AyRIAACACkyUAAEAEJksAAIAI2QafnMVdtcitFpHVor63mN6mbZgyYXjXoUxJd+/eDWL92PfSa02nrk/ldCftAahatCkzgbq2kteh6swz0aj8e/uudlLKlKRMUJ6BRmlTJqVUI15bcgx86rnqh1FJ1UVOi75UStayqgOv7lKNYl5ru5p4mlVc1cuRI0eCmHcdOe0+ebMEAACIwGQJAAAQgckSAAAgApMlAABAhCIdfA4cOCDjyoyjzARqYbp2ZwtvYTf1vP3oKuItUiszgjIl7XSU6UrVUKqpJgVlGhgbG5Of/ctf/hLEem30UnXnGXxSzQ/KRFWyvr39NhXKDJR6v+/cuSPjbcxVqu5yzIVKc619Fpvw9mZ99uxZEFPjiNLnmS/7garTHBNbzrXwZgkAABCByRIAACACkyUAAEAEJksAAIAIRQw+3iL1X//616TvK4NCSRNHDqnGBtVVxDN7lDJL5ORELeCrmHfMnM4WTXgL6+qeq3rJ2d6pFF53GBVXBoHUrYRK4Zk4vHgnqm5LGnzUsTzTTzfb9XlmjX5s6fbgwYMgNj8/H8RKdvBRx/KOr8yCKn/9GIc9I6OqZzVmqHr26uq3pq09e/bY1NSUq4s3SwAAgAhMlgAAABGYLAEAACIwWQIAAERgsgQAAIhQxA2r3GBm2tWkHE3KhdWvvRdVyzW1N6S6ttpuWC/PyhGW6oT0HMud39+1a5eNjo4mHfO35LhhVe5v3bqVfc5eomr32rVrPdXg5VjVqGoFlrNHbRvUs+zVnapxdR3qmP1y0Ct9at/R2q5chXfO1HZ+/dDsjV2pv65Q42237U3NeLMEAACIwmQJAAAQgckSAAAgQtOa5e7kg+zRh5mcnAxi+/btC2IjIyOpp2oiWW8T6lrUdUxPTwexFteRpdlbM1T6UlH3w+zXNcrfMjQ0tPV/Zmn2OmKoa5mYmAhiu3d3fVt3d/wtisp9gfX2LK0qb2Y69+Pj4+0UxcnSPDw8LOOpz5qqnxZr6kVqInWc63ymWpKl2atFVRsqf/3QXGOcy6wNqXdoc3PT+8IJM/spU1M/Ofn1L5rrMmiaT5rZExuseh60HJuhuVeguT5bY8Y2mt4sF83sezP72cx+qSSqBN+Y2bf2q14zNNdi0DR36h2Eeh60HJuhuVeguT6derfBm2V/QXN9eLPsDWjuDWiuT/ab5evUI1+5ckXGnz59GsSOHj0axNRvq9TnIiTrNTNbXl6W8UuXLgWxM2fOBDHvN4+ZuJqVPqXNzOz58+etBahrMzNbWFjwvuJqvn//fhC7ffu2/KzKX+p1XLx4UcaddYnXHX9b8/DhwyB248aNIHbv3r0g1rSbgcDVqnJ07tw5+VkvT50obbOzs0nf/Q1Z+VW1YqZ/MzozMxPEVP1k5tgsU/PZs2dlXI1VV69eDWJtfqcsyNLsPX8KdU9Uvan6NtP36Suu5tXV1SDm/W5YXYvKvard1GfhK1Jv02T5JfXI7969k3E14B88eDCIffr0KfVUTSTrNTP7/PmzjL969SqIVdwmytWs9CltZt1ta/T27dvcr7iaP378GMQ8zWtra0EsNc8bGxtJn/vKl46/rVGaVY17tZWBq1U9K0tLS/Kzqfks1AAkK7+qVsx0PtX4UiDHZpmavVpWBqvMGs0hS7OajDzU9amxZX19PUeCWYNmlaeVlRX5WaVF1W7ONTtIvfx0BAAAIAKTJQAAQITs3rCqb9/du3flZ1V/RNW/UcW83bJL9Yz1+g8uLoZGKBVTPQVL9lFM1WFmdv78+SD2pz/9KYgdOHAgiHk9E9ugeuN6mrvp4+n1cyyVf++fL1XPV5W/Ur2AFUrbhw8f5GevX7+edEz1nHr9Ymv3OVaosUDl3Xum29T4gwcPgphXy+qeqJ7BhXwOWSgdHkqf+r43NrfpMayO7/WAffToUevvl8g9b5YAAAARmCwBAAAiMFkCAABEYLIEAACIUGTzZw+10KoMAupz3sJ0qUXysbExGVcmmFTNJQ0+79+/T/6sMjAcPnw46XMlyTF/qE2IU80ytTcrfvz4sYwrg0fqhrSlyDG4qRyr56emIclMG788U5Iyq6mxQNWKN2Z4P3JvQo0DHuq5V+fsh8HHe+aVZpU/VW8lxzl1fM9gp541ZS797rvvuhcm4M0SAAAgApMlAABABCZLAACACEyWAAAAEZgsAQAAIhRpd+eR6rJTjqgjR44kn6cNnmPqz3/+cxC7fPlyEFMOv5J4LaUUSp/izp07Qayksy2HW7duBTHlQPRaKdbEcyIrfamtEEuR44ZVOVaOR/VMl3RO52hWbRpTj3n69Onk88RQ91A5zM3S2wqq3Nd+/rxaVLlSTuTabm91/d7Yp8bc+fn5INbG/ZwCb5YAAAARmCwBAAAiMFkCAABEYLIEAACIMLS5uen9b783sxedQWWA8Ra4G469/URiEdprXdXQ6mzLERRorkFqCzyzRrOEq1ktcnvHVzlRi9zKyOG1lmogK8+eIUy1O1MGg5x9Cx2OmNnfzKlndf2eKUJpVqYfdT+8enbML1k59gwN6tipreNamCSyNA8NDcn4s2fPgpjSp2JeO7kGE02WZu9ZSX1WVd16tdxgisoaM7x9Y1++fBnEUsfrFvR0bFa580xDzrO+NWZsgzdLAACACEyWAAAAEZgsAQAAIjBZAgAARKi6n6VCLZKrxebaey92izITKPOTWbsuGKmmBjOd0xbGnSp4hiy14K4MNLXrIMfgoz6baqrwaqNEtxHP2KL0Kh2197NUOrz9ItVYkNrNyjOzlMIz3agaVzFVy97Y0KazT84euyqnDx48CGK19oasicq9Z6TKyTNvlgAAABGYLAEAACIwWQIAAERgsgQAAIiQbfBRi6deBx+1sK8WVNVif862PiVRC9/qOtRivbdVVufWMnv27LGpqalsbd4itTJ4qK2j1BZdJVF58gwsyoyg6qAfWxh5mtW2RqojTq/NVcqYYWY2NzcXxFJNPyVRz7Iyc5npGlXPpBqHao8ZXp5V16Hjx48HMaXZy32bus/pHKXqXl1HbYOPurfetSsDl8qzOuaFCxfyxXXAmyUAAEAEJksAAIAITJYAAAARmCwBAAAiMFkCAABEKOKG9RxTY2NjQezUqVNBLHN/wiJ0OlS3UNennGPKVXjs2LEuVf0fSp9yY5ppF+m1a9eCWG1nqXKheU5ppVnVQT/aHnot+pSDVzn0arp6Vd2pfUDNtDtU1VU/nOfz8/Myrhzlanwp0SYwF/VMeSh9ygFccsxQz4rnzL57924Qq+2WVyjN3vOnnL3qmVTfV/NOLrxZAgAARGCyBAAAiMBkCQAAEKFpzXJ36kEmJiZk/PDhw0FscnIyiA0PD6eeqolkvWa/dtFRTE9PB7FDhw4Fsf379wex0dHRpHPt3v3/pbqalT6VT++8FdehXM0jIyNBLEdzoTroZHfH39bs3bs3iKnrK3BtrtZdu8L/vlU16+lQ3y9EVn69Z0XlU40vha4jS7MaBzw2NjaC2OrqalfH/EpWbeSMzWpMK0RWnsfHx2VcdT1TdXTw4MEgllkvUu/Q5uam94UTZvZTzhn6zMmvf9Fcl0HTfNLMnthg1fOg5dgMzb0CzfXZGjO20fRmuWhm35vZz2b2SyVRJfjGzL61X/WaobkWg6a5U+8g1POg5dgMzb0CzfXp1LsN3iz7C5rrw5tlb0Bzb0BzfbLfLF+nHvnSpUsyrv49eXl5OYipXTNmZmZST79Fst4mbty4EcTu378fxJ48CXLprsM0UESz4ty5c0Hs4sWLQezMmTO5h+5pno8ePRrE7t27l3Oq1x1/oyhtZma3b9/OOe82FhYWZNzJf1aOc/SqfKq6mJ2dzZFg1qBZrdWdOHFCflblqcVYkEqRWlbXd+XKlSCm1tyuXr2ae7oszWq8NTM7e/ZsEFP6bt68GcRUDUXI0qzyaaZrRmlW40Pm2Cz1Nk2WX1KP/PbtWxn/9OlTEHvz5k0QW19fTz1VE8l6m1hZWQliS0tLQUwt4LegiGaFyvPa2lqJQ/c0z95ifwZfOv5GUdrMzF6+fNlaRGbus3Kco1cZvz5+/JhzOg9Xs3pW1L02KzYWpFKkltX1qTFx3759JU6Xpfnz588yrvKvTDBqDG9BlmZvbE3VXGBslnr56QgAAECE7HZ3Cq+lkmqtpVoRqTZu79+/l8cs9ZMIr8XerVu3gphqldSvzakVKs+PHz9O+m7tzV29PKsWgmoj3NptzVTtqhZaZrqtnLoO1eJPbaxrVib/XkvA1PZ8amPckq0RVY69zZ+9lo6dqJ8+5NRaSVQbNrVRdMnWdqnkbOyt8qTG69qbm3sbVquaSd1wvsQG57xZAgAARGCyBAAAiMBkCQAAEIHJEgAAIEIRg48yDZjphVpvH8lOahtoPM3KOKCuQ33fW0QutSejt7CeasbohynJ25vOi3eicq/2zTRrl+fUPR89Ug1IXr2VwLv/qh7VXptqb8OS5OxXqwxPqfe1tvHEu47UGkit+bao58K7t2rvSlVHtffAVTXq5Xlubi6Iqd/oq2fNu44c8xdvlgAAABGYLAEAACIwWQIAAERgsgQAAIjAZAkAABChiBvWcxpdvnw5iCnH2qNHj0rIcFHuKq/dlroW5Y5U7aw8t6nXvqkJdU4vz6mt7Wq7YVWevdZx3bhQS7YvUw5CT7P6bKrT03NKe+cqwfHjx4OYyrtygJdkbGysq++r66jdplE9a56zVGlJbWJfkhw3cFEr0aoAACAASURBVOqzptymXi23aSmncuK5n9Xx1feVZu85zXH78mYJAAAQgckSAAAgApMlAABABCZLAACACEUMPmpB1UMtyNZuA5VjolAL36nXV2LPtC3UgrRnEFDXp/ZerJ1nhdof1Ey3XfNMV51497NNay51LLUfpYe6DmX4KFkbqSgdykyn6sJrKdjGXKV0eAYddV7V5qz2HrPKlOcZ9ZRmZQCsva+mGjM881Zq+8XaLQSPHDkSxDzzUer9VQahNibLTnizBAAAiMBkCQAAEIHJEgAAIAKTJQAAQIQiBh+vO8L8/HwQU4YKtR9cjmkoRup+c2a+IaUTtXBecgE/Z285tQivzDKeaaMUyiiyubmZ/H2VP1UvpfYHNdPGGy/Pyoygvl+ydkujnoWcblE5e1M24Zm0lDFGmVGUYWMn590sb5/UNqg8eWNf6lilTDUljVTK6KXMiWb6/qaOGSXGPt4sAQAAIjBZAgAARGCyBAAAiMBkCQAAECHb4JOzwK+MGGrxtR+L9d7Ct1q8Vh1d+tGRxSO1y0Ztg0EOqYv1Jc08qeR0+2jTNag03jOp4qnbjNXOu5fjCxcuJH2/H3XhobbjUtR+/lROPDOOqltlEFLjXKoJsi3eM6WuT40Zi4uLQezOnTvdyuLNEgAAIAaTJQAAQAQmSwAAgAhMlgAAABGYLAEAACJku2GVI8lzpilXk3Iv5bSjq02qs7Qfe0N6pGreSQ5C5QxM3WOvNl4rNtWGq2Trr7Z4z49yvqrnTzmTa7u9veOrNpLKObuTnr9jx44FMXUd/dDsuY5T2zSq2vL2Ii2FV8/Kta3GvmvXrgWxEq513iwBAAAiMFkCAABEYLIEAACI0LRmuVsFd+0K59eJiQl5gKmpqSA2OTkZxEZGRhpkJCP15jI+Ph7E1PrDnj1Fdjcronl4eDiIKc2F1teKaFY1Mzo6WuLQnezu+Bvl0KFDMn7w4MESelLIynG3z18/6kJp8yg0PiiK1LIaC9T17d+/v8TpsjR7uVN1MD09HcT6odlDPZdKX4F6lnqHGvYbPGFmP3V71h5y8utfNNdl0DSfNLMnNlj1PGg5NkNzr0BzfbbGjG00vR4tmtn3Zvazmf1SSVQJvjGzb+1XvWZorsWgae7UOwj1PGg5NkNzr0BzfTr1boM3y/6C5vrwZtkb0Nwb0Fyf7DfL192e8eHDh0Hsxo0bQUz9+/7NmzflMRvWOrrWa2b2/PnzIHbu3LkgdubMmSB29epVecyGtbgszUqbmc7p06dPk47p5Xl2dtb7SpZmT4eKq99XLSwsBDGV+wZed/xtzerqahA7e/Zs0nfVdZiZHT16VIWztC4vL8u4qlt1DaoGMnNsVuj5U6Rex7179+T3Sz1/HkqLqmV1n7y6aKCI5itXrgQxNb6onLbwFriaVe7UeGam55OZmZkgpuo5U7PU2zRZfsk5umJtbS2IqYJRC+SfP3/OPV3Xes3MPn36FMSWlpaC2Lt374LYxsZG7umyNCttZmZv3rwJYqnbBn38+DFHglmm5vX1dRlXPyZWmlUNZfKl429r1P31JqpOvHvnkKXVe1aUNpX3Ajk2K/T8KVR9q+uo/fx5qPOurKwEsbdv35Y4XRHNavx69epVEGuRU4WrWR1faTPT4/Af/vCHpGNmIvXy0xEAAIAITJYAAAARivxY0Ovll9p/UPUv9HYVV70tS6I0q56ld+/eDWJe/8FSPSG9PKvfFc3Pzwexy5cvBzGvD2qJXopNx1e7rauejmqH89q9KT1U7ap+u6p2vTyU6Nfr9VlN/ad41fPWe/5q98JV1/L48eMgduDAgSDm9UiurVk934uL0lBZFXX93nOc+tnauVN15o3x6vlT/Y/VeK36yubCmyUAAEAEJksAAIAITJYAAAARmCwBAAAiFDH4eIvAavFVLSwr80O/NipW+pQBSWn2TBGl8DZyVSgtyiBUewH/9OnTMq7yrMwdqQYas/rmL6Ul1fRTCvVMKbOZmTbuKNT31XnMypnVPOOJdy2dqBzXvv8eqQa72pvcq2fqwYMH8rOnTp0KYqqWa6Puo/f8qGtRY6LKQwnzF2+WAAAAEZgsAQAAIjBZAgAARGCyBAAAiMBkCQAAEKGIGzanpZJqRdQPl6aH0uI5Azsp6cZTzi/V+s1Mu8dSd/Wo7YDzWtOp1naqJVVth3EOKleqXpTmUnlObWFnlu6erp13dfxU16uH527sB+r61FhQ+1nLuWf9Gl+7QY1/qg7UeF3ienmzBAAAiMBkCQAAEIHJEgAAIAKTJQAAQIQiBh9vsV0Zf1S7rFIttEqgFodTjR0lr+PRo0dBzGtd5cVT8EwgtVtzqVyp1njKCFTSSKXMGd7edyqu6kW1QuyHoULdW/VMqnzWNtCodnBm2qym6qIfrdm850xdSz8MPjmoWlbtJnfSeK3yV2KfylR4swQAAIjAZAkAABCByRIAACACkyUAAECEbIOPWgS+fv26/OyxY8eCmDI/1EYtAqtOQmZmHz58CGJzc3NBzOtaVAqVZ0+zyumtW7eCmOqA0Y/rMNPmk8OHDwex48ePF1a0HdX1xKtnhcppTQOE2ofwwIED8rPKpJVq5ilpSMoxiaQai2p3dlK5u3z5cvL3vW5bOwU1zqlxRD0L3rXVHktUzShDmBpzcvYC9uDNEgAAIAKTJQAAQAQmSwAAgAhMlgAAABGGNjc3vf/t92b2ojOoulgoA4yZ3k5IbdmUakSIcOTr30CzQi0Mm5ktLi4GMWWgUIvZ3gK3dy7L1OyhjD+qs0whU0SW5qGhIRlXZgJVR2phPtNAc8TM/mZOPSu8PKUaGJTBwKtnJ56VY8/4ldrZSdV3iw4+RWpZnXdsbCyIqc5OnpmsAVezMgV65kT1WTWOqLHP6+rTUONZefY6cSmzkupEpJ4/rzYaxpcszd6WiOq8Sp/a/u39+/fymI6RbWvM2AZvlgAAABGYLAEAACIwWQIAAERgsgQAAIjAZAkAABAhu92dcnSpmJl2KqmYcvN57YkanKVZeI6rVBecinmOx1Kavb3blOuxH20FFV5rLHXPVSu3UrnLwbuPKqep+3J696PE3pw5e48qx2LtvUtzUO5EVRe19zHsdh/H1L0Xa+9zmrOHZqqbWLlNS+K5zlN/qXD+/PkgViLPvFkCAABEYLIEAACIwGQJAAAQoWnNcne3B9+/f38Qm5ycDGL79u0LYsPDw7mn61qvmdnIyEgQGx8fD2JTU1NBbHR0NPd0WZqVNjO9tdXevXtztaSSpVnVgJnWrGpj166u/3tud8ff1igthw4dCmKq00jm/cjSumePfownJiaC2KdPn4KYV1eZFHn+FKouClFNsxozVK30a5xTY9X09HTSd1uMLVmaVZ7M9HOlruPgwYM5p1NIvU3t7k6Y2U/dnrWHnPz6F811GTTNJ83siQ1WPQ9ajs3Q3CvQXJ+tMWMbTW+Wi2b2vZn9bGa/VBJVgm/M7Fv7Va8ZmmsxaJo79Q5CPQ9ajs3Q3CvQXJ9OvdvgzbK/oLk+vFn2BjT3BjTXJ/vN8nXqka9cuSLjDx8+DGLq35hv3rwZxGZmZlJPv0WyXjOz+/fvy/jt27eD2PPnz4OY0jw7O5sjwSxT84kTJ2R8eXk5iKk1VfWbq5KaVZ7Onj2bfGCl+eLFi0HM0+ysGb/u+NsaVTOq9u/duxfEMuu5a61mZjdu3Ahiq6urQUzVcguKaFb5VJoXFhZKnC5LsxrPzHSenzwJxtpSVKsNxdWrV0ucrsjYrOKqNnLGDAept2my/JJ65Hfv3sn40tJSEFM/Dl1fX089VRPJes3MPn78KOOvXr0KYmqrMe/7mWRpVpOimdanqK1ZmUdStXmoh2FjYyPnEF86/rZG5U9dX4F67lqrmdnKykoQa7H1VipFNKuxZKdoXltbk3HvuaxEtdqoSJGx+c2bN0FM1UaBcU7q5acjAAAAEZgsAQAAImT3hlV4vfxUL0XVh1L10nzxQm+q3aaXpuoDe+HCBflZ9fs/1X9Qfd/bsb5U/0evz6O6PtW/UWn2eq+26cmq7s3c3Fzy91U/YLWju6ctp3dnE94/+6naVbXR6362Xm/XW7duBbH5+fnacpLwalnVrddfuNd4ufOe+52A1wNb1UbOs1oK9cx7Y7PSlzq2e2NDznzCmyUAAEAEJksAAIAITJYAAAARmCwBAAAiFDH4eIunavFVbeCpFm5LbIq7hTJceJvxqo2s1aao169fD2KeMaS2wUdt/py6QWvJPKvr9MwnKv7hw4cgVntDaHXPcjafVXVUe0PfTryN0o8dOxbEvGvrNYOo2TPL7JTNs5U+z3ykNkhW16E2Cy85ZnT7G1p1zaqGSmjmzRIAACACkyUAAEAEJksAAIAITJYAAAARmCwBAAAiFHHDeqQ6kHrdHsxMu167peLuCI0o95fi2rVrQazXzs0tlMtOoVyTJTUrB6ByF5tpB6GqI+Xe9BzjJZyeXi6Vi7tf97sTT0c/xgKFepaVW9ts52hWtezt+vOnP/0p6fuqhrx6a1NbyuH/448/ys+qsUDdk1ruZN4sAQAAIjBZAgAARGCyBAAAiMBkCQAAEGFoc3PT+99+b2Z6U8kuUIYGtWDsLfI2cOTr30CzaonkGS68RfwUvP3gGhacXc3doq5PmRa8PDcs1hfRnHpPlMHAa/vncMTM/mZOPatzPn78WB5IGaRUTtVegaptn5mbfzfH6vNqP1iz9L02VUu0zBybNWhWOfLMf0qfukdqHGnR0ixL89jYmDyI2ntXtUFMvbYIrmY1jnr3UdWRGvuUebBfY4bKlbrnXivFDLbGjG3wZgkAABCByRIAACACkyUAAEAEJksAAIAIPTf4pC6cP3r0SH6/YUHcXURWHVmUWcPTp7pgpO57adbY4aOawSfVCDI/Py+/32DwqKZZnVMt1md2Smo0+ChThHe/ujF/ZeY5y8Rx5MiRIGamTUWqRpUBzTNrNJgnsurCe449c1UKqsOSWXh9u3btstHRUbNMU+Dx48dba/PolylQHf/y5ctB7NmzZ0GsRceiLM3evqEq/2qeaGGa6gSDDwAAQBuYLAEAACIwWQIAAERgsgQAAIiQvUWXMld4xhZlKHn//n3SebxF3jaLt8qM423Rldr5pvbWUQpv6yi1yK06iNRG5SmnE8zdu3eTPufVRputklQHEM9AlGqaUrXVoiOOROn1zGqpWxqpY9auH9U1yEwbfLzuR5149dPZ7WdkZMRmZmYaj6VqSXVE8lD5U/dDdXsyq7fN1BZqrErt+FSbnE5MLbo2tYY3SwAAgAhMlgAAABGYLAEAACIwWQIAAERgsgQAAIiQ7YZVLirPOadciyqm3IOeW64U3p5syo2nWpXVdr4qPNfj4uJi0vdVOzC1L2BblIvUc64qzcr1qFpw9cOhZ+ZfSyeeO7wW3vmUU1DVsmqhV/v589zBSotykaoa8MahAu3PGo+vniHlklb17bVBrI2qDeWUVg5875cEpfDyrM6LGxYAAGAHwWQJAAAQgckSAAAgQtOa5e7Ug0xNTcn45ORkEJueng5iExMTobA92cupyXrNfu3ioTh8+HAQ+7qdTw2yNB86dEjGU7esOnjwYBDbtSv7v5dczeqe5WhW9bJ3794cbYrdHX9bo+pA1cvw8HC3p+paq5nZ/v37g5jK8efPn4PY+Ph47umKaFbnVWNGoVopMmZ4418nSnOLsaVIntW1qFou8PyZZWpWdWum54lKSL1N+1meMLOfqskpz8mvf9Fcl0HTfNLMnthg1fOg5dgMzb0CzfXZGjO20fT6tmhm35vZz2b2SyVRJfjGzL61X/WaobkWg6a5U+8g1POg5dgMzb0CzfXp1LsN3iz7C5rrw5tlb0Bzb0BzfbLfLF/XUHHixIkgdvHixaRYBFfv6upqEDt37pz87PLychA7evRokgBP85kzZ7yvZOVYXYeZvhal+ebNmzmn88jK86VLl5I/e/Xq1SAW2x0igdcdf6OcPXs2+eDq3s7Ozgax1HWtr1R59szMbty4EcSePn0axH744YfcQ7uanz9/HsTUc2am9al1PfWsqbxHqJZnVfcqzwsLC/L7DXWfpfnKlSsyrvKvarT2mKFQeTLT16LGOS+nGUi9TZPll27PqFA3yZsEMnH1bmxsBLFXr17Jzy4tLQWxVLPD2tpa0ud+Q1aO1XWY6WupuBielec3b97IzyqDz/r6eheyXL50/I3i1YZCXYcyzGRS5dkzM1tZWQliOdfbgKv506dPQcx7VtT4oBqAfPz4MUebR7U8v337NoipsaVFzWdpfvfunYyr59IzMBUgS7OXE1UbyrRYAKmXn44AAABEyP59Rg6qJdXLly+DmGpxVRLVpsxrEee1lOtEtVkq2QZKbf6qWr95qOtT96PUpsRmOs+qfaCHahH27NmzIFay3Z1q55XaPtD7rGql6LVXrIl6rrzNhjvxfo7Ups1jzqbHqiWcetbUMUu2bsxB1b23UXsnXqvCNvWidKRuqG6mn1WV01LtA8205pxWiyrPakwrsZk2b5YAAAARmCwBAAAiMFkCAABEYLIEAACIUMTg4y2spxolau9JphaRjx07Jj/b670IPVL7vZrpa1EmGHVtJQ0+NVAL88rc0RZlKDlw4ID8rMppP4w7qajnb25uLoipfJbcrzXHkKXut6rRfuwn66H2X1R9VpW5sSSqFr1aVp9V16Fyn7qvawrqnN58kLo/sjIgeeN6Th3xZgkAABCByRIAACACkyUAAEAEJksAAIAITJYAAAARst2wyq3mtVRSreOuX78exHLaG7VBOUu9FnvKuac+u5OcpcpRlvo5z9nWpqWccqHduXNHfvbChQtBTDkIVW2VdMMqN5x37aqO1POg3OH9cG+mtl9MrZ+2qOfbaz+m4qoNm1dX/eD48eNBTI0ZqpZLtuhT9enVsoqrmHrWSrZC7PY4qS08vRrPyT9vlgAAABGYLAEAACIwWQIAAERgsgQAAIiQbfBRC6JHjhyRn33//n3SMVXrpZIL32rB12upNDY2FsTUnoqpraHaokwDXusqhbq+nHZtpfaM9O5j6v0dGhoKYp7mUvvsecdR5jS1x6iqjX60xVPmrfPnzwex2i0ec0xUygSjNNfeu1KZWDxjmbq3ap9F1ZayX3twppKzN+ROaRWqKLFnMm+WAAAAEZgsAQAAIjBZAgAARGCyBAAAiJBt8FGL9V6nkJ2y15/SnLOwPj8/n3TMkqh9Fj1UnpVJRXVC8RbrdwrKFOF1HSpl8PGMCur4ysxz69atIFaqU5K6X8pk5KGe1dqdp5RZpnbXoG5RNaDuq4fqRlV7PFSmwG7zXHsP1xzNqo562RmLN0sAAIAITJYAAAARmCwBAAAiMFkCAABEyDb45OB1ydkJeB0d1HZCamHZM2yUQi1cewaWnA5FnZTq1GOm8+Rt56PiyjjQj9x7mj98+BDElBlBdVoq9Syoe+0ZLlSeVGcZZRryaq1NvahaVrk008a22tu0KXK2WVNaXr58GcSUaaikwU6Zt+bm5uRnlRYVU9dWclxXBr6c7ROVFlX3JfLMmyUAAEAEJksAAIAITJYAAAARmCwBAAAiMFkCAABE6LkbVrndlKOw5D5vyh2lXK9m2gWonFS9bLO0hecAVHlWjs5r164VVhQ/p3cfVes91SJMXVvt9mze8ZUrU3Hnzp0gVrNeclqaqWtTLkjvvpVyb6o9Ys3SWxYqV6/XdrMNynnpOYFVTlX+ctoglmop59Wyqhl1fd22Co2hnm/vOUv9pULq/ciFN0sAAIAITJYAAAARmCwBAAAiNK1Z7q5xwsnJySA2Ojpa4tCu3uHh4SA2NTUlP3vw4MEgtmtXtf+myMqxp2N6ejqIqZwWWjdzNe/ZE5aTut9men1S3RP1fXU/G9jd8TeKqgEzrVmxf//+1FN5VHn2zMzGx8eDmKof9bkIWZq9e6i0rK6uBrG9e/fmnM6jSJ7VczkxMRHEVP14z0cDWZq9sVWdd9++fUnfHxkZyZFglqnZu7cqf5XGOal3aHNz0/vCCTP7qduz9pCTX/+iuS6DpvmkmT2xwarnQcuxGZp7BZrrszVmbKPpzXLRzL43s5/N7JdKokrwjZl9a7/qNUNzLQZNc6feQajnQcuxGZp7BZrr06l3G7xZ9hc014c3y96A5t6A5vpkv1m+7vaMaq3h7NmzQUz9u/O9e/fkMRvWN7P0Pn/+XMYvXboUxJaXl4OYWl978iTIb4yuc2xmduXKlSD28OHDIKZyevTo0dzTuZpVnlQ+vc+eOXMmiM3OzgaxmZmZRoEdvO74uw1Vo+fOnZMHUpp/+OGHIOath2dQpC7Utf3jP/5jEFtYWAhi6l5EyNKscmmm61b9tlPluPaY4XHjxo0gdvv27SCm9GXWslnFMUPVi6qNFmRpVnOEmR6z1b1VmluOGdtomiy/5BxdsbGxEcTUQ6IWZNV3I2Tp/fTpk4wrfWq7nUJ0nWMzs3fv3gWxpaWlIOZdcyau5s+fPwexV69eyc8qfeo61tfXc7QpvnT83YaqsxzN6poLUKQu1LWpWl5bWytxuizNXt7UgK3yrkw1tccMj5WVlSCm8lygls0qjhne1nQFyNLsPX8qp2o7vIJjxjb46QgAAEAEJksAAIAIVXvDKtSrtIrl7JbdBq9XoPonYRVbXAwNU57mUjuLe305VS9F1SezVO481HVev35dflb984nq6aj6QXr9NNvkWfXI9O6jQt2TUv1Tu0X131WoXrYl+6wqvB6w6h6qZ1XdNy/vqvdtDPVPkt5xVM/XY8eOBbFS40AO3rOixozz58/XlpOEVxtqLFB1cPr06SDm9SLOGRN5swQAAIjAZAkAABCByRIAACACkyUAAECEbIOP2nRVGQTMutvAtLYZxdOmzDzKeKJMILUX8L3Nn5VZxvtsr8kxiqj81TZSKQOEt2GuOm+pTXprMD8/328JLl7eUu+hZ1wphRp/vN9bqwbfyozSD4NPzsbgO2XMyDHIpV6fV28YfAAAAArCZAkAABCByRIAACACkyUAAEAEJksAAIAI2W5Y5bz0nEYfPnxofczaeK2rlMtOxdS1eS30SrnMPBeoag+lXL07HeW0PnXqVBDz2mG1QbXGUu5GM+2S7XWelVPQcwSmtrsrmc9UunWGqnZ03RxzdXV1264l6vjeOKXa3Sk3rDpm7daI3tjs1fhORuVPueXVmOE53HPgzRIAACACkyUAAEAEJksAAIAITJYAAAARsg0+ygygFl7NtIlG7W/YZr+5HNQit1qUz0G1cSuxiNyEZ5hSxh+V051gUGlC7QFYW5+6j14rNWWY8Vo91kK15/KeP4W6htqtJZVxSxlgumVsbKz1d0dHR7f9/2q/R09z6rX041nzTIGqdZ/SpwxInpGxNkqfMl3VaivImyUAAEAEJksAAIAITJYAAAARmCwBAAAiZBt8cvAWlzup3UFEHf/Ro0fys6obioqphe/a+9V5HURUFwsVU5q9DiL9WMRXRomc/fjaoMwn58+fl59V+a9hVGlC1bL3/ChDlzL41K5bZdzy7uuLFy+CmOqApUxN6jxtUcYvpc1M14B6/mobABXevVUGH2X0ytHcjzFD6avVFYk3SwAAgAhMlgAAABGYLAEAACIwWQIAAESoavBJNQ6ojim1u4p42pSZQC1c1zZFKDwzieo2orbgUYv6XvekTtPInj17bGpqqlGfMl14Rg5l/lK5r53n9+/fBzGvU1I3Bh+ve0tNA1NOZ5+aqHvo3VelWdWoqvnateIdP/W8/ejg49VnqtEr9X6YlTP4eB20VFyZedTz65l+cgxMvFkCAABEYLIEAACIwGQJAAAQgckSAAAgApMlAABAhKpuWOWOUu4/5UjyWniVcrx5rfjU8Wvvt5mK5+hSLjvlLFV4ruM2eVbOOU+Hyr/Sknodbclpsac0K1eh4tSpU1m6SqCeK+UoVK3Z+uH2NtNjhoqpdnQQ4rk9VS2rfX9VHdRu8eiN/Z5LvRNVGyWcurxZAgAARGCyBAAAiMBkCQAAEKFpzXJ31wffEx7+0KFDQWxjYyPpuxGy9I6MjMi40rdrV7X/psjS7OkYHx8PYtPT00FsdXU1iE1MTORIMGvQrO7Z5OSk/Oznz5+TtBTI/e6Ov9Hjezn59OlTEEvtkuPlwaHrZ8/MbHh4OIip+t67d2+J0xXRrHKv6rsQ1TSrWilEEc0qp6o21LXt378/93RZmtXYZabHL0WBcUTqHdrc3PS+cMLMfso5Q585+fUvmusyaJpPmtkTG6x6HrQcm6G5V6C5PltjxjaaXt8Wzex7M/vZzH6pJKoE35jZt/arXjM012LQNHfqHYR6HrQcm6G5V6C5Pp16t8GbZX9Bc314s+wNaO4NaK5P9pvl627PqP6N+dKlS0FsZmYmiF28eFEec3R01Dudq/fp06dB7MqVK/Kzy8vL3mG2oTQvLCzIz7bRrLhx44aMq+tTub969WoQO3PmTI4EswJ1Yabr4OHDh0FM5TRT8+uOv1GeP38u4yr/Kvezs7NB7ObNm6mnN+txjtVv8XJ2Y/iKq1nVoveb4du3bwcx9fyoGsjMsVmhPKt6Ubn/4YcfgljD2ODhalZj19mzZ+VnU9f/jh49GsS8ca5hV6KsPHvaTpw4kXROledMpN6myfJLt2dUxp03b94EMWWSUN+N4OpdX18PYt6kqLaxUqgf65bUrFhZWZHxV69eBTGV07W1tZzTeXRdF2Zmb9++DWIq9wU0f+n4G8UzZ6jaVZrfvXuXeiqPnua40FZermb1XHi1rPSprdEK5NisUJ5VvajxpcX4oHA1K9Pc0tKS/GzqD/xVwxN1nghZefbypK6lkvlS6uWnIwAAABGYLAEAACJU7Q2r+lCqXpoq1mLNxCVnp3Z1XrW+ojR7PUXb9CVUfRpv3bolP3v+/PkgpnKvejo2GLyq0o9d4xWqR6bXUToxNQAABOxJREFU+1LVjOr56vUdroXXP/fBgwdB7NixY0Gsdq9P9Vx4tXzt2rUgpmrl8uXLQcwbM7z+x6VQz3c/euuqPOXUsqoj1TfYq7faPbTVPx0rfaruS/QS5s0SAAAgApMlAABABCZLAACACEyWAAAAEYoYfLzfaaWadNTia0kDiFrMVgYaM704rH77pUw1JTYY3UJtgKrMGWbaQJGaP+/elcq/l+e7d+8WOX63KIOAt/msMjaoe17od4vJ5BiKlOGjHwYYzwyncqyePzVm1DbVeI0UVA2p60vd8Lwt3WwCb2Z2/fr1IKZ+41rSfKnodsP3WhuD82YJAAAQgckSAAAgApMlAABABCZLAACACEyWAAAAEbLdsMrp57lAlUss9Zj9Qrm/FLUdhArVws6LKxeqahHmOSnbXJ9yWip3cQ6HDx/u6vsxlHPOc9OpOlV5Vnnw8lzCwek5SxUlHdupqLx5+VDO1zt37gSx2tehnimvnVuq+/L48eNB7MWLF/Kz/WiXp1DO19qtKnPcsN4vBGrAmyUAAEAEJksAAIAITJYAAAARmCwBAAAiFDH4eAYdtTedaqm0Uxazc9gp+zGaaTNOqmmqpFHpwoULycdPbWvWjzx7Rg5Vuwq1V6N3P7pt7WWW1+5Ome760SYuR3M/zHSqFtV+ih7KlKTw2kH2w4ilzHSqPkvuW6lqI9UY2mt4swQAAIjAZAkAABCByRIAACACkyUAAECEbINPzt6QCrWgu5MMPspMoLr6qK4p/ViU90g1RXhdgdqYKnK64ZQwttQipx5VBxFVB6X2AFTGmBzjieoupGq55J6AqnONZ9xS+pShJKdrURvU9XumHVXLjx8/DmKqVvphXvJQWlQHrpJ74KpnJWev4V7CmyUAAEAEJksAAIAITJYAAAARmCwBAAAiZBt8clALtcqM8Mc//rGmDLkgrYxGZukGitqdZZRmz3hy9+7dIPbs2bOk8/SrE5EyE6iuKf3AM2qpDkWqq09Jc0wn6n6dP39eflbVhWJubi6IlbwGdSxPs6oLtbWcMqbVNst4daFMSepZVd8vqVmNXd7YquootXNOyW39lA5vbFYGn152++HNEgAAIAKTJQAAQAQmSwAAgAhMlgAAABGYLAEAACJUdcMqp5Nq+VQb1XoqdW9CM93uznNslULlzttHTjkLlYNXuR771WowtbVW7f30FF5bLVW7NZ2vClUXXutA5VpUz0Lq3qcl8Vyayvmq9sXdSW3iVP5yWhDWxLu3ynmu9rNUe7PWzr3n0Ff61HXUckrzZgkAABCByRIAACACkyUAAECEpjXL3d0efHh4OIgdOnQoiI2MjHR7KrMGvXv37g1i6t+/PUZHR4PYrl1F/jsjK8dKh5nZ9PR0EFtdXQ1i4+PjOafz6LouzPS6hLonBToM7e74G0XVi5mu3UoUyfHk5GQQUzn26iqTLM0TExMyXqkGPIrkec+ecBjtR56VDjU2mOnxYWpqKoh5z0ImWXn2xlalT6HmnUyk3qHNzU3vCyfM7Kduz9pDTn79i+a6DJrmk2b2xAarngctx2Zo7hVors/WmLGNpsnyd2b2z2b22sy+1NPVNbvN7B/M7D+//v9orsOgaf6t3v+1wajnQcuxGZp7BZrr0zlmbKNpsgQAAADD4AMAABCFyRIAACACkyUAAEAEJksAAIAI/w8w9G8peNaP8QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 576x576 with 100 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_digits(digits.data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "现在有大约 1800 个 64 维度的数字，可以创建一个 GMM 模型来生成更多的数字。GMM\n",
    "在这样一个高维空间中可能不太容易收敛，因此先使用一个不可逆的降维算法。我们在这\n",
    "里直接用 PCA，让 PCA 算法保留投影后样本数据 99% 的方差："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1797, 41)"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.decomposition import PCA\n",
    "pca = PCA(0.99, whiten=True)\n",
    "data = pca.fit_transform(digits.data)\n",
    "data.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "结果降到了 41 维，削减了接近 1/3 的维度的同时，几乎没有信息损失。再对这个投影数据使用 AIC，从而得到 GMM 成分数量的粗略估计:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x216b3874d30>]"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_components = np.arange(50, 410, 20)\n",
    "models = [GaussianMixture(n, covariance_type='full', \n",
    "                         random_state=0) for n in n_components]\n",
    "aics = [model.fit(data).aic(data) for model in models]\n",
    "plt.plot(n_components, aics)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "在大约 190 个成分的时候，AIC是最小的，因此我们打算使用这个模型——立刻用它拟合\n",
    "数据，并且确认它已经收敛："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n"
     ]
    }
   ],
   "source": [
    "gmm = GaussianMixture(190, covariance_type='full', random_state=0)\n",
    "gmm.fit(data)\n",
    "print(gmm.converged_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "现在就可以在 41 维投影空间中画出这 100 个点的示例，将 GMM 作为生成模型："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [],
   "source": [
    "data_new, y_new = gmm.sample(100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100, 41)"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_new.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 100 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "digits_new = pca.inverse_transform(data_new)\n",
    "plot_digits(digits_new)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "简单回顾上述操作步骤：首先获得手写数字的示例数据，然后构建该数据的分布模型，最\n",
    "后依据分布模型生成一批新的示例数字。这些“手写数字”并不会单独出现在原始数据集\n",
    "中，而是获取混合模型输入数据的一般特征。这个数字生成模型同时也可以证明，生成模\n",
    "型是贝叶斯生成分类器的一个非常有用的成分。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This section is accomplished!"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
